In petroleum exploration and development, formation evaluation is used to determine whether a potential oil or gas field is commercially viable. One factor to determining the commercial viability of a potential field is the resistivity of the earth formation. The resistance to electric current of the total formation—rock and fluids—around the borehole is the sum of the volumetric proportions of mineral grains and conductive water-filled pore space. If the pores are partially filled with gas or oil, which are resistant to the passage of electrical current, the bulk formation resistance is higher than for water-filled pores.
Conventional induction logging tools use multiple coils to measure the conductivity (i.e., the inverse of resistivity) of the formation. However, formation conductivity is not a single number because the formations are invariably anisotropic, i.e., directionally dependent, which causes the conductivity to be a tensor quantity. As a result the more recent induction tools have been designed with multiple transmitter or receiver coils whose magnetic moments are in multiple directions and measurements between these coils are sensitive to more than one component of the conductivity (or more generally, impedance) tensor.
For instance, in 3D array induction imager wireline tools (e.g., 3D-AIT™), both transmitter and receiver coils have magnetic dipole moments in the x, y, and z directions, with z defined as along the axis of the tool. This is an improvement of conventional induction tool design, where only z-directed coils are employed. As an example, energizing the transmitter coil (T coil) in the x-direction and measuring with a receiver coil (R coil) that is in the y-direction provides the xy-component of the coupling tensor in the tool frame of reference. Other combinations of the transmitter and receiver coils can provide remaining components of the coupling tensor and characterize the formation.
Similarly, LWD (logging-while-drilling) tools may be designed with receiver antennas having magnetic dipole moments tilted relative to the z-direction and transmitter antennas having magnetic dipole moments parallel to the z-direction. The tilted receivers may be, for example, in the z- and x-directions and provide measurements that are a linear combination of those two signals. As the LWD tool rotates during normal drilling operations, the tilted receivers sample formation properties in multiple directions and can provide many, but not all, of the components of the coupling tensor. As the tool penetrates the earth, other earth layers come within the depth of investigation of these measurements and the distance to these boundaries can be extracted from the measurements and used for geosteering purposes.
An inherent difficulty in using these tools is that the coil efficiency, and electronic drift affects the coupling between T and R coils. Thus, the T-R signal is not just a function of the medium filling the space between the T and R antennas, and needs to be corrected for coil sensitivity and drift. With current designs, for example, there are no extra measurements available to enable one to estimate these couplings (e.g., gains) and one must assume that the gains remain constant and uphole measurements (e.g., calibrations) can be used to correct for them.
In logging, the borehole compensation (BHC) technique provides a method of self-calibrating electromagnetic measurements. BHC consists of placing two outer sensors symmetrically on the two sides of the center sensors. For four coils, made of two transmitters and two receivers, the coil arrangements along the tool axis are either T1-R1-R2-T2 or R1-T1-T2-R2. By taking appropriate ratios of four basic and un-calibrated measurements, one can create a quantity that is independent of coil gains. The method is based on taking two ratios leading to Equation (P1) below:
                                                        (                              T                ⁢                                                                  ⁢                1                            )                        ⁢                          (                              R                ⁢                                                                  ⁢                1                            )                        ⁢                          S              11                                                          (                              T                ⁢                                                                  ⁢                2                            )                        ⁢                          (                              R                ⁢                                                                  ⁢                1                            )                        ⁢                          S              21                                      *                                            (                              T                ⁢                                                                  ⁢                2                            )                        ⁢                          (                              R                ⁢                                                                  ⁢                2                            )                        ⁢                          S              22                                                          (                              T                ⁢                                                                  ⁢                1                            )                        ⁢                          (                              R                ⁢                                                                  ⁢                2                            )                        ⁢                          S              12                                                          (                              EQ            .                                                  ⁢            P                    ⁢                                          ⁢          1                )            where the antenna efficiencies are shown in parentheses and Sij represents the desired signal received from transmitter i by receiver j.
As can be seen, R1 is common in the first fraction and the gain of R1 receiver cancels in taking the first ratio, the gain of R2 cancels taking the second ratio, and when the two ratios are multiplied together, the gain of T1 and T2 cancels. The net result is a ratio measurement that, if expressed in logarithmic form, leads to an amplitude ratio and a phase shift, both of which are gain corrected. In this example, because the coils or sensors are aligned with the z-axis, only the zz-component of the measurement tensor is determined. This method works well when the antennas are arranged symmetrically as in CDR™ (Compensated Dual Resistivity) and EPT™ (Electromagnetic Propagation Tool) devices.
For logging tools attempting to characterize the whole coupling tensor, the sign (or phase for complex quantities) of off-diagonal terms is very important as it is used for log interpretation purposes. The BHC method works by taking ratios of the measurements, which introduces sign ambiguity. Examples include the ratio of two negative terms and a negative ratio in which it is not clear which term had a negative sign originally. For LWD tools with receiver coils that are tilted relative to the z-direction, the tool rotation may be used to generate gain-corrected signal ratios. This technique partially solves the problem, but limits the measurements to simple ratios of electromagnetic coupling tensor elements.
Therefore, it is a desire to provide a method of measuring the entire coupling tensor, which is the preferred way of inferring earth conductivity anisotropy and the distance to boundaries separating media of different conductivities. It is a further desire to make these measurements in a gain-corrected fashion with minimum requirements on the hardware. The present invention proposes a solution to characterize both the coupling tensor and the gain corrections.